Hofstadter Triangle

For a Nonzero Real Number $r$ and a Triangle $\Delta ABC$, swing Line Segment $BC$ about the vertex $B$ towards vertex $A$ through an Angle $rB$. Call the line along the rotated segment $L$. Construct a second line $L'$ by rotating Line Segment $BC$ about vertex $C$ through an Angle $rC$. Now denote the point of intersection of $L$ and $L'$ by $A(r)$. Similarly, construct $B(r)$ and $C(r)$. The Triangle having these points as vertices is called the Hofstadter $r$-triangle. Kimberling (1994) showed that the Hofstadter triangle is perspective to $\Delta ABC$, and calls Perspective Center the Hofstadter Point.

See also Hofstadter Point

References

Kimberling, C. ``Hofstadter Points.'' Nieuw Arch. Wiskunde 12, 109-114, 1994.

Kimberling, C. ``Hofstadter Points.'' http://cedar.evansville.edu/~ck6/tcenters/recent/hofstad.html.